相关论文: New theory of periodical systems by finite interva…

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time…

New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…

We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…

Damping typically results in attenuation of vibrations and elastic wave propagation in mechanical systems. Contrary to this conventional understanding, we demonstrate experimentally and explain theoretically the revival of an elastic wave…

This paper is concerned with the time-dependent Maxwell's equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we…

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…

A problem of a wave identification is formulated. An example is considered in conditions of one-dimensional Cauchy problem for conventional string equation in matrix form and its inhomogeneous two-component version. The acoustic and…

We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic systems described by the nonlinear Schrodinger equation with a sinusoidal potential, such as photonic crystals, waveguide arrays,…

In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications,…

A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…

We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…

The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction…

Oscillations are ubiquitous wave phenomena in physical systems ranging from electromagnetic and acoustic to gravitational waves. The behavior of finite-size systems is traditionally understood to be governed by fundamental oscillatory modes…

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the…

Key properties of a physical system depend on whether it is gapped, i.e. whether its spectral gap has a positive lower bound that is independent of system size. In quantum information theory, the question of whether a system is gapped has…

We develop a theory to compute and interpret the photonic band structure of a periodic array of metallic helices for the first time. Interesting features of band structure include the ingenuous longitudinal and circularly polarized…

This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em SIAM J. Appl. Math. \bf78} (2018), 1737-1753), by utilizing spectral properties of the…

We consider the operator ${d^4dt^4}+V$ on the real line with a real periodic potential $V$. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define a Lyapunov function which is analytic…

Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in…

This paper introduces a novel deep neural network architecture for solving the inverse scattering problem in frequency domain with wide-band data, by directly approximating the inverse map, thus avoiding the expensive optimization loop of…